Abstract The computation of the Campbell diagram of a rotor modelled by using a large number of degrees of freedom involves much computational work, particularly when damping is not neglected. The aim of the present paper is that of developing a computational technique, based on a fast converging, iterative, modal approach solution of a model which is partially uncoupled. After the modal analysis of a non-gyroscopic undamped system having the same inertial and elastic properties of the rotor has been performed, the damping and gyroscopic matrices are split into a “proportional” and a “non-proportional” part. If the latter is negligible, modal uncoupling is performed and the computation of the Campbell diagram becomes very easy. If the non-proportional parts of the relevant matrices cannot be neglected, a fast converging iterative procedure allows one to plot the Campbell diagram in a fraction of the time needed by the usual techniques. This procedure can also be used for the computation of the damped eigenfrequencies of natural systems and is particularly suited for the study of the influence of any variation of the damping characteristics of the system on its dynamic behaviour.